@Kitonum It never dawned on me that shadebetween( ) accepts variable limits. Thanks so much!

@acer yes, this is exactly what I needed. Given how rationalize( ) works, it makes sense that we have to use the reciprocal. Thanks!

@Preben Alsholm This is a nice, efficient solution. I never knew about "freeze." I always seem to learn something here, thanks!

@Kitonum Thanks for the multiple approaches.

@Rouben Rostamian  Thanks for the work around. What's the procedure for reporting a bug? i've never done so.

@Carl Love I am working with matrices with integer entries, so I naturally made the assumption that they are all integers, however, this property does not require integers.

@Markiyan Hirnyk This is just what I needed. Thanks for a nice, simple solution!

@Carl Love It can be shown quite easily with such restrictions on the entries, the eigenvalues will be c+d and a-c. It's a nice little trick to have the eigenvalues be integer valued, without going for the obvious triangular approach.

@Kitonum Yes, I am aware of how to do it using the formulas for projections, etc. 

@Carl Love I wish I could upvote your comment!

@Axel Vogt I don' think learning math is the goal here ;-)

@Carl Love The polynomial in the question is x^3+x^2+2*x+1, but you used x^3+x^2+x+1.

@Carl Love I typically always work in 2-d mode, hence, I always use y'(x), p''(t), etc. :-)

@mehdi jafari I've tried the command with a trigonometric function in Maple 16, 17, and 18. It works fine in Maple 16, but fails in 17 and 18. So it appears to be a bug introduced in the newer versions of Maple. It would be nice to hear from a developer. :)

This is what I tested:

Student[Calculus1]:-Tangent(sin(3*x),x=0,output=plot,gridlines=true,caption="")

@mehdi jafari But yet, this works fine.

Student[Calculus1]:-Tangent(exp(-x^2),x=0,output=plot,gridlines=true,caption="")

I wonder why. Any ideas?